GATE CE 2020 Set 1 — Question 15
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Structural Engineering → Determinate Structures & Energy Methods → Trusses (Joints & Sections)
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Question
Consider the planar truss shown in the figure (not drawn to the scale)
Neglecting self-weight of the members, the number of zero-force members in the truss under the action of the load , is
Correct answer
(C) 8
Solution
To find the zero-force members, we apply the following rules:
1.At a joint with two non-collinear members and no external load or reaction, both members are zero-force.
2.At a joint with three members, where two are collinear and there is no external load or reaction, the third member is zero-force.
Applying these rules to the truss:- At the top-right joint: Both members are zero-force (2 members).
- At the joint to the left of the top-right: The vertical member is zero-force (1 member).
- At the joint below the top-right: The diagonal member is zero-force (1 member).
- Continuing this analysis for the remaining joints without the load or reactions, we find a total of 8 zero-force members. The load is effectively carried by the members in the first panel directly connected to the supports.
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